People value intelligence and will apply that label to themselves even if it may not be true. It's a hard thing to measure though IQ does it reasonably well. To those who have a high IQ: what is it like? Can you pick up any book, read it, and understand the gist with minimal repetition? Can you infer solid and accurate conclusions based on a small amount of evidence? Is any subject or discipline up for grabs or do you have to have a keen interest in a particular field in order to flourish? What is something you are able to do that you know is because of your intelligence -- the proverbial 1,000 pound deadlift of the brain, if you will.
There is no point to these questions other than curiosity.
My dad's entire (big) family is over 160IQ, which is statistically unheard of. All of them can grasp anything they put their mind to. They only put their mind to things that interest them. As far as I can tell, only one or two of them are smart enough to see the forest through the trees and be immune to marketing and propaganda, because it interests them to put their minds to those sorts of things.
They're all boomers, and like most boomers they have largely been failures as far as their families go; although, I'd say that's mostly because of women being allowed to be batshit insane. Their intelligence hasn't really helped them avoid batshit crazy women.
As far as the various example tasks you mentioned, they're all skills that can be trained and require both interest and discipline. Some require a baseline intelligence, but it's not substantial. Sherlock Holmesing conclusions from mere minutia is a bit fantastic, though.
Personally, I slept through AP Calculus and aced it, but that's because I liked the math and spacial reasoning, and I sometimes did my homework (usually during lunch). I had previously flunked out of a 6th grade advanced math course called MEGSS because I was bored and uninterested (it was basically pre-algebra for 6th graders, and I would have ended up taking AP Calc a year earlier).
Conan Doyle even made it a point to state that Holmes willingly kept ignorant of certain things that didn't help him in his endeavors. I believe that was demonstrated through him not knowing the Copernican model of planetary movement and saying he'll just immediately discard it because it doesn't matter if he knows it or not.